In a non-magnet (NM)/ferromagnet (FM) double layer nanostructure, in-plane current of an NM layer may generate a torque known as a spin orbit torque (SOT) that is enough to reverse magnetization at an FM layer. Many studies have been made to confirm that main mechanism of the SOT is one of spin hall effect (SHE) of an NM layer and NM/FM interface spin-orbit coupling (ISOC). In a system in which an NM/FM interface is perpendicular to z-axis and in-plane current flows along x-axis, spin current polarized along y-axis is generated based on spin Hall effect induced by bulk spin orbit coupling at a non-magnetic layer. The spin current is injected into an adjacent FM layer to transfer a torque to magnetization of the FM layer. A spin orbit torque (SOT) induced by the spin Hall effect generates a strong damping-like torque (TDL∝m×m×y) but generates a weak field-like torque (TFL∝m×y). Theoretically, it has been known that the strength of SHE-induced SOT is independent of a magnetization direction of the FM layer. In the case of ISOC-induced SOT, a spin polarized along y-axis is accumulated at the NM/FM interface by broken inversion symmetry. Direct exchange coupling between magnetization of the FM layer and the accumulated spin generates a strong field-like torque TFL but generates a weak damping-like torque TDL.
It is known that unlike a strength of the SHE-induced SOT, a strength of the SOC-inducted SOT is dependent on a magnetization direction of the FM layer. In the two cases, the SHE and the ISOC qualitatively induces the same torque on the FM layer. To confirm a dominant mechanism of SOT, a damping-like torque TDL and a field-like torque TFL should be quantitatively analyzed for a wide-range magnetization angle.
A harmonic hall voltage measurement method is one of the methods useful in quantizing the effective field of TDL and TFL originated from SOT. This method is especially suitable to identify angle dependency on vertical magnetization of SOT applied to an FM layer. Several revisions including planar Hall effect (PHE), an out-of-plane component of an external magnetic field, and anomalous Nernst effect (ANE) are required to accurately analyze a measurement result. In measurement of a harmonic Hall voltage, a second harmonic resistance R2ω includes two main components of anomalous and planar Hall magnetic resistances (represented by RAHE and RPH, respectively). When an external magnetic field Hext is applied in a longitudinal direction (x), R2ω values caused by AHE and PHE are in proportion to TDL and TFL, respectively. However, while a transverse (y) Hext is applied, the R2ω values caused by AHE and PHE are in proportion to TFL and TDL, respectively. To this end, use of an analytical expression based on Cramer's rule is needed to separate TFL and TDL from each other. The analytical expression was successful only in a system having RPHE<RAHEIn the case of a system having RPHE>RAHE such as triple-layer structure of W/CoFeB/MgO, divergence occurs in an analytical expression to make it very difficult to analyze a measurement result.